Non-equilibrium quantum matter

Lead Research Organisation: University of Cambridge
Department Name: Physics

Abstract

The understanding of non-equilibrium quantum systems is one of the greatest challenges of modern science, as recognised by the EPSRC Grand Challenges Programme. Its development will have profound effects across different research areas including quantum computation and information, quantum optics, and biology. Theoretical understanding of these systems will form the basis for future development of new generation fast and energy efficient microchips and instruments for precise measurements.

The occurrence of non-equilibrium behaviour is very common in Nature. The simplest example of this can be found when two objects with different temperatures come into contact. Other systems can show various levels of complexity from the physical process that leads to emission of a laser beam to the ultimate case of living organisms. The common characteristic property of these systems is the absence of uniform thermodynamic quantities such as temperature.

Some of the state-of-the-art experiments in this field are made with semiconductor nano-structures in high magnetic fields and very low temperatures. In these systems electrons move in a coherent way similar to photons in a laser beam. Remarkably, because of strong interactions, the electrons in these systems form new strongly-correlated emergent states which exhibit quasi-particles with only a fraction of the electron charge. Similar quasi-particles also occur in quantum magnetic materials in the so-called spin liquid states. In the future it is hoped that these particles will be used as fundamental building blocks of topological quantum computers. The problem of quantum motion of a large number of quasi-particles is in the class of non-equilibrium quantum problems, whose study constitutes one of the main aims of this research programme.

Interestingly, many of these systems show non-equilibrium steady states. Take a piece of metal and connect it on opposite sides to a heater and a refrigerator, a configuration which will result in a steady heat flow. A similar situation occurs in a system of interacting electrons in a quantum wire connected to a battery. The important differences with the former arise from the fact that the motion of particles in the wire obeys the laws of quantum mechanics, which lead to unusual quantum states. Recently it became possible to study these states in experiments, which resulted in a number of unexpected observations e.g. PRL 96, 016804 (2006); PRL 105, 056803 (2010). Next generation experiments will build quantum devices that use and explore the physics of non-equilibrium states based on the new theoretical and experimental insights.

The project is aimed at theoretical understanding of quantum systems which are driven far from equilibrium by, for example, applied voltage or fast switching of external fields. In this setting many physical systems with examples ranging from semiconductor nano-structures and superconductors to quantum magnets and ultra-cold atomic gases show remarkable emergent behaviour (see for example PRL 105, 056803 (2010), arXiv:1308.4336, Science 331, 189 (2011), Nature Physics 8, 325 (2012) etc). This comes as a result of intricate quantum entanglement which occurs in these systems due to motion of interacting particles under non-equilibrium conditions. The properties of these systems cannot be explained using standard theoretical framework, and it is the one of the central tasks of this project to develop this theoretical description.

Planned Impact

Condensed matter physics has been the driving force of the tremendous progress that we see today, from the invention of a transistor, that revolutionised our lives, changed the way we think, work, and communicate, to lasers, that brought important advances in medicine, industry and computing. Things such as magnetic resonance imaging (MRI) and levitating trains as well as many remarkable advances in precision measurements came as a result of research in superconductors. The theory of condensed matter systems had profound impacts of its own in many branches of science including biology and particle physics. The concepts of broken symmetry, the theory of phase transitions and the idea of Higgs boson, which originated in superconductor studies, represent some of the most remarkable examples of deep connection between these fields.

From this perspective, being on the leading edge of fundamental research, the proposed programme will provide scientific competitiveness in the immediate future, and in the long term societal impacts and will contribute to UK economic growth. Learning how to create and manipulate the properties of strongly-correlated systems will offer a completely new window of opportunities, which has a potential to overshadow the semiconductor revolution.

This research proposal is in the field of theoretical condensed matter physics and its immediate impact will be in theory and experiment within academia. This includes research groups in the UK and internationally affecting a large number of scientific areas. The project has a potential to stimulate the development of new experimental directions in the UK in the fields of mesoscopic systems and cold atoms. The programme will also contribute to sustainability of condensed matter and cold atom experiments in the UK.

The field of quantum computations will benefit from this research on a number of levels. First, the project will provide theoretical understanding of the properties of electron quantum optics devices, the experimental development of which is one of the first steps on the way to quantum computers. Second, the theory of non-equilibrium edge states in electronic systems and cold atoms is an essential ingredient for understanding how to create and manipulate quantum states in these systems.

The traditional computer industry will start to benefit from this project in the next 10-15 years. With decreasing size, exponentially growing number of components and ultra-fast transistor switching times in modern semiconductor microchips, the industry is fighting increasing problems of heating and occurrence of errors. Without understanding of energy transfer, dissipation, and decoherence on a microscopic scale these problems cannot be solved and it is a task of the project to provide a fundamental basis to make this solution possible.

This programme will also contribute to improving the quality of training of young physicists through discussions, collaborations, seminars; training of PhD students and supervisions of postdocs, and publication of the results in scientific journals. I will use every opportunity to disseminate my research to a general public through the Cambridge University web-site, public lectures organised by the University, and through the Cambridge Science Festival.

The new analytical and numerical toolbox which will be developed in this programme will benefit experimentalists in mesoscopic physics and cold atoms, and the research in the strongly-correlated quantum systems and quantum chemistry.

The theory of quantum systems far-from-equilibrium is in its early age and the aim of this project is to transform this situation, bringing the UK into a world-leading position in this field. This is an extremely hard problem, but the impacts would be huge.

Publications

10 25 50

Related Projects

Project Reference Relationship Related To Start End Award Value
EP/M007928/1 01/10/2014 09/06/2016 £757,607
EP/M007928/2 Transfer EP/M007928/1 01/08/2016 31/10/2019 £532,741
 
Description 1. We developed the theory of a dynamic (non-equilibrium) response in Kitaev quantum spin liquids. These novel states of matter, which have been predicted theoretically more than 40 years ago, have only recently been found in experiments. One of the most exciting spin-liquid states is Kitaev spin liquid, which host unusual fractionalized quasiparticles -- Majorana fermions. By using our theory predictions to analyse the neutron scattering experiments by our collaborators (group of S. Nagler, Oak Ridge National Lab) we showed, for the first time the evidence for Majorana fermions in proximate Kitaev spin-liquid material \alpha-RuCl_3 (published in Nature Materials). In addition our theory of Raman response in Kitaev quantum spin liquids agrees well with experiments, adding further support for fractionalized excitations in proximate Kitaev materials (Nature Physics paper).

2. We discovered a large and exact degeneracy in quantum magnets with Skyrmion excitations, which is a new and unexpected result. This system is described by a model which has been extensively studied in condensed matter, and high energy physics, and is one of the important toy models describing topological excitations. Recently we have generalized our theory to other classes of Skyrmion magnets (paper in preparation),

3. We found an expression for the exact time-dependent Green function of the non-linear Luttinger liquid theory in terms of the fourth Painleve transcendent. The non-linear Luttinger liquid theory, which has been developed recently by Imambekov and Glazman, cures the major drawback of linear Luttinger liquids, and is an important development in the field of low-dimensional quantum systems. However, the exact expression for the Green function, which is one of the main ingredients of the theory, was not known. In our paper we have provided this missing piece of the theory.

4. Since 80th people tried to find systems, where Anderson localization physics can arise without presence of quenched disorder. In our recent work on Disorder-free localization we presented the first example of an interacting quantum system, where disorder arises dynamically from quantum fluctuations of some of degrees of freedom (far from equilibrium), and leads to complete localisation of other degrees of freedom. There are many interesting extensions of our work, including higher-dimensional systems.

5. We linked the physics of gravitational anomalies to the infamous sign problem showing for the first time that sign problem is unavoidable in local quantum Monte-Carlo simulation methods.

6. We showed that interactions destroys precise charge quantisation in the experiments with quantum Hall emitters. These finding are important for experimental efforts on quantum optics experiments with electrons.

7. For the first time we calculated the OTOC (out of time order correlators) for a microscopic model (essentially in the thermodynamic limit).
Exploitation Route 1. Our work is relevant to ongoing experiments which study quantum spin liquids states in novel materials. Kitaev spin liquids host Majorana fermion excitations, which may be used in quantum computations. The work is also relevant to theoretical physics community, as our results can be extended to a larger class of materials, and theoretical methods can be used in the studies of other non-equilibrium systems.

2. Our results on Skyrmion magnets are important to both theoretical condensed matter and high energy physics communities. There are many interesting new directions to explore in the context of our theory. There are also ongoing experimental and theoretical efforts to study Skyrmions in magnetic systems (e.g. MnSi), to which our theory may bring some new insights. Skyrmions may also be used in future spintronics applications.

3. Our work on non-linear Luttinger liquids is an important contribution in the field of low-dimensional systems, as it provides a missing ingredient for the universal theory of non-linear Luttinger liquids of Imambekov and Glazman.

4. Our recent work on Disorder-free localization is a important contribution to the fields of non-equilibrium physics, Anderson localization, and Many-Body localization

5. Our work on quantum-dot emitters is important for electron quantum optics experiments, and for the theory of spin-boson models.
Sectors Electronics

URL https://www.nature.com/articles/nmat4604
 
Description Our theoretical results for dynamic structure factor of Kitaev spin liquids have been used by experimentalists to analyse their data, and to provide evidence for Majorana fermions in proximate Kitaev spin-liquid materials. Our work with experimentalists published in Nature Materials has been selected 18th in the Top100 discoveries of the year by Discover Magazine. Our work on Sign problem and gravitational anomalies has been advertised in a large number of national and international newspapers. Altmetrics score 724
Impact Types Cultural,Societal

 
Description PhD studentship funded by EPSRC (PhD student Adam Smith at TCM)
Amount £1 (GBP)
Funding ID EP/M508007/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2015 
End 10/2018
 
Title Theory of Kitaev quantum spin liquids 
Description we developed a theory of dynamical (non-equilibrium) response in Kitaev quantum spin liquids. Analytical tools and insights which we developed can be used in the context of other systems with fractionalized excitations. 
Type Of Material Improvements to research infrastructure 
Year Produced 2015 
Provided To Others? Yes  
Impact recent experimental confirmation of our theoretical predictions provides evidence for Kitaev quantum spin liquid behaviour (and the signatures of Majorana fermions) in novel magnetic materials. First neutron scattering experiments on these materials have been recently done at Oak Ridge National Lab in collaboration with my group (paper accepted for publication in Nature Materials). we obtained for the first time exact dynamic structure factor (non-equilibrium response) for a strongly correlated quantum system in two and three dimensions. Our work also provides a classification of dynamical response in 3D Kitaev spin liquids. 
URL http://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.115127
 
Description collaboration with B. Doucot 
Organisation Sorbonne University
Country France 
Sector Academic/University 
PI Contribution theoretical research collaboration
Collaborator Contribution discussions, research
Impact research papers 1. Multicomponent Skyrmion Lattices and Their Excitations, D. L. Kovrizhin, Benoît Douçot, and R. Moessner, Phys. Rev. Lett. 110, 186802 (2013) 2. Large and exact quantum degeneracy in a Skyrmion magnet, B. Doucot, D. L. Kovrizhin, R. Moessner, arXiv:1601.04645
Start Year 2011
 
Description collaboration with J. Knolle, TCM 
Organisation University of Cambridge
Department Theory of Condensed Matter
Country United Kingdom 
Sector Academic/University 
PI Contribution we have a number of common papers together. both of us contributed extensively to these papers. Johannes Knolle is my former PhD student, and we continued our collaboration after he moved to TCM group, Cambridge (Johannes is currently funded by Marie Curie Fellowship).
Collaborator Contribution we have a number of common papers together. both of us contributed extensively to these papers.
Impact the list of papers which we published in this collaboration is listed in the papers section.
Start Year 2015
 
Description collaboration with N. Perkins 
Organisation University of Liverpool
Department Department of Physics
Country United Kingdom 
Sector Academic/University 
PI Contribution theoretical physics collaboration
Collaborator Contribution discussions, collaboration
Impact a paper Phys. Rev. Lett. 113, 187201 (2014)
Start Year 2014
 
Description collaboration with Oak Ridge National Laboratory 
Organisation Oak Ridge National Laboratory
Country United States 
Sector Public 
PI Contribution collaboration on experiment done by collaborators. my contribution was the theory (in collaboration with other theorists)
Collaborator Contribution experiment
Impact research article to be published in Nature Materials, http://arxiv.org/pdf/1504.08037v1.pdf
Start Year 2015
 
Description collaboration with Prof. J.T. Chalker, Oxford University 
Organisation University of Oxford
Department Department of Physics
Country United Kingdom 
Sector Academic/University 
PI Contribution common papers, discussion
Collaborator Contribution common papers, discussions
Impact common papers, see publications
Start Year 2007
 
Description collaboration with S.E. Nagler 
Organisation University of Tennessee
Department Bredesen Center for Interdisciplinary Research and Graduate Education
Country United States 
Sector Academic/University 
PI Contribution experiment
Collaborator Contribution theory
Impact a paper http://arxiv.org/pdf/1504.08037.pdf, accepted for publication in Nature Materials
Start Year 2015
 
Description collaboration with T. Price and A. Lamacraft 
Organisation University of Cambridge
Department Theory of Condensed Matter
Country United Kingdom 
Sector Academic/University 
PI Contribution we have published a common paper. all members of the research team discussed the paper, and have done the calculations.
Collaborator Contribution we have published a common paper. all members of the research team discussed the paper, and have done the calculations.
Impact a research paper "Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent", Tom Price, Dmitry L. Kovrizhin, Austen Lamacraft, SciPost Phys. 2, 005 (2017).
Start Year 2015
 
Description collaboration with Zohar Ringel, Theoretical Physics, Oxford 
Organisation University of Oxford
Department Rudolf Peierls Centre for Theoretical Physics
Country United Kingdom 
Sector Academic/University 
PI Contribution we have been working on a common project, the paper is due to be submitted soon
Collaborator Contribution we are writing a paper
Impact not yet
Start Year 2016
 
Description collaborations with J. Nasu and Y. Motome 
Organisation University of Tokyo
Country Japan 
Sector Academic/University 
PI Contribution theoretical physics collaboration
Collaborator Contribution discussions, papers
Impact paper http://arxiv.org/pdf/1602.05277v1.pdf, submitted to Nature Physics
Start Year 2015
 
Description partnership with LPN/CNRS group of F. Pierre 
Organisation National Center for Scientific Research (Centre National de la Recherche Scientifique CNRS)
Country France 
Sector Academic/University 
PI Contribution discussion with the members of the group of their experiments
Collaborator Contribution the group contributed experimental data, discussions
Impact publications related to experiments done by this group
Start Year 2009
 
Description partnership with R. Moessner MPIPKS Dresden 
Organisation Max Planck Society
Department Max Planck Institute for the Physics of Complex Systems
Country Germany 
Sector Academic/University 
PI Contribution theoretical research partnership
Collaborator Contribution discussions, writing papers
Impact see list of publications
Start Year 2010
 
Description EPSRC Network Plus on Emergence and Physics Far From Equilibrium 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Participated in Network Plus discussions of the roadmap document
.
Organized an international workshop in Oxford on non-equilibrium physics, as a part of Network Plus activities.
Year(s) Of Engagement Activity 2014,2015,2016
 
Description Graduate lecture course on Phase Transitions and Critical Phenomena 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact I have delivered a new graduate lecture course at TCM on Phase Transitions and Critical Phenomena, which contributed to engagement in discussions, and communications between PhD students at TCM.
Year(s) Of Engagement Activity 2015
 
Description Journal club seminar series joint between Quantum Matter (QM) and Theory of Condensed Matter (TCM) groups 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact This is an ongoing seminar series suggested by me, and organized together with Malte Grosche (QM group). The task of these informal seminars is to bring together the experimental group (Quantum matter) and Theory of Condensed Matter group (TCM) to discuss questions of common interest, possible future experiments, etc.

The informal atmosphere of the seminars provides an opportunity for lively discussions during, and after presentations.

The seminar series helped to establish new communication channels between experimentalists and theorists working at QM and TCM groups, and there is a potential to generating new collaborations.

In addition the seminars also help PhD students to improve their skills in presenting their work to a broader audience.
Year(s) Of Engagement Activity 2015